In Unit 5,
students solve for unknowns in area, surface area, and volume problems. Students
find the area of triangles and other two-dimensional figures and use the
formulas to find the volume of right rectangular prisms with fractional edge
lengths. Students use coordinates as they draw lines and polygons in the
coordinate plane, and find the distance between points as they solve
real-world problems.Students
represent figures using nets.

Standards:

Supporting Clusters

Geometry

6.G.1

Find the area of
right triangles, other triangles, special quadrilaterals, and polygons by
composing into rectangles or decomposing into triangles and other shapes;
apply these techniques in the context of solving real-world and
mathematical problems.

6.G.2

Find the volume of a
right rectangular prism with fractional edge lengths by packing it with
unit cubes of the appropriate unit fraction edge lengths, and show that the
volume is the same as would be found by multiplying the edge lengths of the
prism. Apply the formulas V = l w h and V = b h to find
volumes of right rectangular prisms with fractional edge lengths in the
context of solving real-world and mathematical problems.

6.G.3

Draw polygons in the
coordinate plane given coordinates for the vertices; use coordinates to
find the length of a side joining points with the same first coordinate or
the same second coordinate. Apply these techniques in the context of
solving real-world and mathematical problems.

6.G.4

Represent
three-dimensional figures using nets made up of rectangles and triangles,
and use the nets to find the surface area of these figures. Apply these
techniques in the context of solving real-world and mathematical problems.

Enduring Understandings:

·Tools provide ways of thinking
about geometric objects and processes.

·Geometry offers ways to visualize,
to interpret, and to reflect on our physical environment.

·A net is a plane figure that can
be folded to make a solid figure.

·Solid figures can be identified
and classified by the number of faces, edges, and vertices.

·A visual representation of a shape
hierarchy is an efficient way to describe the relationship among shapes with
similar attributes.

Essential
Questions:

·What is a real world
application of surface area?

·How is a net utilized to
represent a 3D figure?

·How is volume affected by
a change in one dimension?

·What are the similarities
and differences between area and surface area?

·What are the properties of
two- and three- dimensional figures?

·What is the relationship
between the areas of rectangles and triangles?

·How is the formula for the
area of a rectangle used to find the volume of a rectangular prism?

·How is finding the volume
of a rectangular prism similar to finding the volume of a pyramid?

·How does the change in
height affect the volume or surface area of a prism?

·How can you estimate the
volume or surface area of a prism or a pyramid?